Question

If z₁ = 1 – 3i, z₂ = – 4i, and z₃ = 5, show that (z₁ z₂)z₃ = z₁(z₂ z₃)

Answer 1

(z₁ z₂) z₃ = [(1 – 3i)(– 4i)]5

= [– 4i + 12i²]5

= [– 12 – 4i]5

= – 60 – 20i  ........(1)

z₁(z₂ z₃) = (1 – 3i)[(– 4i)(5)]

= (– 20i + 60i²)

= – 20i – 60  .......(2)

From (1) and (2) we get

∴ (z₁ z₂)(z₃) = z₁(z₂ z₃)